Alliance:
Druid: Night Elf
Hunter: Night Elf > Dwarf
Night Elves have Shadowmeld, higher base Agility, 1% extra Dodge and 10 Nature Resist. Higher Dodge is amazing for dodging physical slows and getting Mongoose Bite procs (if you're real sweaty). For Dwarves, 10 Frost Resist is really nice but Stoneform and Gun Specialization are basically useless (no diseases in 19s, Serpent Sting does laughable damage, and bleeds are pretty rare).
Mage: Gnome (in all cases) > Human
Gnome Mage is an absolutely insane race/class combo. Higher base Intellect, 5% bonus to Intellect, Escape Artist, and 10 Arcane Resistance (gives you about a 7% chance to resist Polymorph). You will be targeted by so many Pollies that the 10 Arcane Resist will come in handy. Escape Artist is good in so many situations.
Perception on Humans is nice for Mage, but you can usually just spam Arcane Explosion around where you think a stealthed Rogue is anyway.
Paladin: Human > Dwarf
With every poison/bleed being a joke in 19s (and Paladins having Cleanse), Stoneform is borderline useless. 10% Armor may sound nice, but armor has diminishing returns, so the bonus usually only translates to a 2-3% physical damage reduction bonus.
Perception is incredible for Paladins. In general, Horde despise Pallies and their Blessings, so you will almost always be targeted by Saps, Polymorphs, and other CCs. With rogues always trying to Sap you, you can use Perception and spam Judgement while SOTR is up and almost always get Rogues out of Stealth. Once you get them out of Stealth, they will probably Gouge you which means they can't Sap at all and can't Gouge again for 10 seconds. That's a win for the Pally in my book.
Priest: See Bowner's post
Rogue: Gnome > Night Elf > Human > Dwarf
I've never played a 19 Rogue, so I can't provide much insight here. That being said, Rogues are very one-dimensional (scary when not CC'd, but laughably easy to CC). With slows/snares being some of the most common CC in the 19 bracket, Escape Artist is almost never useless. Gnome just always seems like the best. The 10 Arcane Resistance is great for resisting Polymorphs as well.
I will say Night Elf Rogue looks at least somewhat viable. Being able to Shadowmeld immediately after a Sap is very useful and Night Elves are known for being better jumpers as well.
Warlock: Gnome > Human
This is actually kind of a close one I'd say. As a Warlock, you'll be targeted by tons of Polymorphs, so 10 Arcane Resistance is definitely nice. Escape Artist is also great as you are already vulnerable enough and slows/snares oftentimes seal your fate.
That being said, Bowner definitely makes a good argument for Human Warlock. The higher base Stamina is very useful. Also, Perception is incredibly useful as Rogues can completely destroy Warlocks if they have the opener (Kick Fear and Gouge if the Kick was juked).
Warrior: Gnome > Dwarf = Night Elf > Human
Like Rogues, Warriors can be pretty one-dimensional. My brother mains a 19 Gnome Warrior and I can't even tell you how many times Escape Artist was the deciding factor in whether he survived and/or we returned a flag.
Bowner is definitely right about the Dwarf's Frost Resist being really useful. Mages (especially Frost Mages) are going to be one of your major annoyances as a Warrior and being able to resist a Frostbolt / Frost Nova / Frost Armor / Frostbite can put a lot of situations in your favor.
That being said, I hate RNG and will reduce reliance on RNG whenever I can. I would personally go Gnome as you have a slow/snare break on a 1 min CD.
Night Elf is an interesting race for Warrior. The 10 Nature Resistance is useful for resisting Entangling Roots and Nature's Grasp (something I see Warriors get hit by a lot). Shadowmeld is also incredibly useful for getting Charges and avoiding a lot of ranged CC (while you're still out of combat).
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Horde:
Druid: Tauren
Hunter:
Melee: Orc
Ranged: I can see a good argument for any of the three.
I personally prefer Orc. Although the 5% pet damage bonus doesn't make that much of a difference, the 25% Stun Resist is absolutely insane. You won't see a ton of Blackout and Impact stuns, but you will see a ton of Improved Concussive Shots, Charges, and HoJs. Even though you should almost never get charged by a Warrior as a Hunter, being able to resist a Charge usually leads to you being able to get away unslowed. I should also mention that Blood Fury goes really well with Raptor Strike.
Tauren also works really well with Hunter. Higher Stamina is always a plus (although you should be taking less damage in general than other classes). War Stomp is insane on so many levels (creates a gap for Pallies and Rogues on you) and allows for easy flag passes. The 10 Nature Resist is also great for resisting Entangling Roots and Nature's Grasp.
Mage:
CC Mage: Highly debatable
Spell Damage Mage: Troll
99% of people (some of which are incredible Mage players) will tell you to go Undead hands down. Will of the Forsaken and 10 Shadow Resistance will obviously be amazing against Warlocks and Priests.
However, I don't fall in this 99% category. I actually prefer Troll and argue that you should almost never be hit by a Fear or a Psychic Scream as a Mage. I'm making this sound easy and it isn't, but if you have decent awareness then it's a lot easier than it sounds.
Fear is a 20 yard range and Polymorph/Frostbolt is a 30 yard range. This creates so many opportunities where you can Polymorph but they can't Fear. As for Psychic Scream, try and keep a 30-second timer going in your head when a Priest uses it. Avoid standing really close to Priests and try playing around with the max range of Frost Nova. There are many times where I've seen a Mage be able to Frost Nova a Priest before they can get a Psychic Scream off.
The only real benefit that Trolls have over Undead is the Berserking racial. This ability is underrated as hell and can help you get Polymorphs on other Mages (even if you both cast at the same time). The other thing I love about Berserking is that you can use it when you're at half health or so (I can't remember the optimal %) and then throw out Frostbolts and Fireballs like no tomorrow. I also don't know whether this affects the GCD, but if it does, more power to Trolls.
Priest: Undead > Troll
I've never played Priest on Horde, so I'm not going to be able to provide great insight here. Will of the Forsaken is much more useful Priests than Mages as you can't really stand way in the backfield like a Mage can. Also with Psychic Scream being short range, you'll find yourself in range of Alliance players' Fears and Psychic Screams pretty often.
However, Hex of Weakness (Troll Priest Racial) seems objectively better than Touch of Weakness (Undead Troll Priest Racial) and I'm not sure how the Blackout Talent works with them. Berserking is also OP for getting tons of heals off.
Rogue: Undead > Orc > Troll
This is also a really interesting question, but probably comes down to whatever comp the Alliance has. Undead Rogues hard counter Alliance Warlocks and Priests which makes them incredibly OP on offense.
That said, Rogues can already Trinket out of Fears (but not Stuns) which makes Orc Rogues shine a bit. As someone who has played 19 Paladin a bunch, I absolutely hate Orc Rogues (especially as when flag carrying). Many times an Orc Rogue resisting HoJ can be the difference between life and death for a Paladin FC. Blood Fury is also nice in burst situations, but they generally won't have as much melee Attack Power as a Enhancement Shaman or a Warrior.
Shaman:
Restoration: Troll
Enhancement: Orc
Flag Carrying: Tauren
I could definitely go into depth about how each race excels in each of these three roles, but this post is already long enough lol. Berserking is great for getting off heals.
Blood Fury is amazing on an Enhance Shaman with high melee AP (they get 2 AP for every 1 Strength). Hardiness (stun resist) also makes you hard counter Paladins.
Tauren's War Stomp creates for amazing CC (especially against casters when paired with Earth Shock) and opportunities to pass the flag. The higher Stamina is always nice too.
Warlock: Orc > Undead
Like the mage situation, if you truly have good awareness, you should almost never be getting hit by a Fear or a Psychic Scream.
I played a 19 Orc Warlock and absolutely loved having Hardiness. There are so many times when a HoJ or Improved Concussive Shot would be the cause of death for a Warlock.
Warrior:
Flag Carrying: Tauren
Offense: Undead > Orc
Taurens are hands down best for FCing (see above).
As for offense Warrior, this is highly debatable and also depends on the Alliance team's comp. Like Shamans, Warriors get 2 AP per point of Strength, making Blood Fury incredible. Hardiness will also help you stay right on Paladins.
I'm surprised I don't see a lot more Undead Warriors. The Warrior trinket doesn't break fears, making Will of the Forsaken really valuable.